Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Найти угловой коэффициент касательной, проведённой к графику функции y=root( 25)(x) в точке x_(0)=1.

11. Найти угловой коэффициент касательной, проведённой к графику функции y=x25 y=\sqrt[25]{x} в точке x0=1 x_{0}=1 .

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find limits involving trigonometric functionsright chevron icon

Full solution

Q. 11. Найти угловой коэффициент касательной, проведённой к графику функции y=x25 y=\sqrt[25]{x} в точке x0=1 x_{0}=1 .
  1. Calculate derivative: Calculate the derivative of y=25(x)y = \sqrt{25}(x) to find the slope of the tangent line at any point xx.
    y=x125y = x^{\frac{1}{25}}
    y′=(125)x125−1y' = \left(\frac{1}{25}\right)x^{\frac{1}{25} - 1}
    y′=(125)x−2425y' = \left(\frac{1}{25}\right)x^{-\frac{24}{25}}
  2. Find slope at x=1x=1: Evaluate the derivative at x=1x = 1 to find the slope of the tangent line at that specific point.\newliney′(1)=(125)(1)−2425y'(1) = \left(\frac{1}{25}\right)(1)^{-\frac{24}{25}}\newliney′(1)=(125)(1)y'(1) = \left(\frac{1}{25}\right)(1)\newliney′(1)=125y'(1) = \frac{1}{25}

More problems from Find limits involving trigonometric functions

Question
Find lim⁡x→∞x+1x2+1 \lim _{x \rightarrow \infty} \frac{x+1}{x^{2}+1} .\newlineChoose 11 answer:\newline(A) 11\newline(B) 22\newline(C) 00\newline(D) The limit is unbounded
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve the differential equation.\newlinedydx=e2x−2y\frac{dy}{dx}=e^{2x-2y}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of each function using the limit definition.\newlinea. \newlinef(x)=x2+3x−5f(x)=x^{2}+3x-5
Get tutor helpright-arrow

Posted 2 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline2+4x+1+4 2+4 x+1+4 \newlineYou must answer all questions above in order to submit.
Get tutor helpright-arrow

Posted 2 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline1−x+x+2x+3 1-x+x+2 x+3 \newlineYou must answer all questions above in order to submit.
Get tutor helpright-arrow

Posted 2 months ago

Question
What value of y y makes the equation below true?\newline9y−2=25 9 y-2=25 \newline22\newline33\newline55\newline99
Get tutor helpright-arrow

Posted 2 months ago

Question
What value of z z makes the equation below true?\newline10z+5=75 10 z+5=75 \newline77\newline1010\newline1111\newline1515
Get tutor helpright-arrow

Posted 2 months ago

Question
What value of y y makes the equation below true?\newline2y+5=21 2 y+5=21 \newline55\newline88\newline1414\newline1616
Get tutor helpright-arrow

Posted 2 months ago

Question
What value of y y makes the equation below true?\newline4y−5=23 4 y-5=23 \newline66\newline77\newline1414\newline2323
Get tutor helpright-arrow

Posted 2 months ago

Question
What value of y y makes the equation below true?\newline6y−1=17 6 y-1=17 \newline33\newline66\newline1515\newline1616
Get tutor helpright-arrow

Posted 2 months ago

View all (90)